Faculty of Engineering
Assiut University
2022/2023
May 2023
Fault Diagnosis and Failure Analysis in
Mechanical Systems
4th year Mechanical Engineering
Students
Vibration Analysis
(1) For the following equations:
(a) Prove the equations.
(b) Use MATLAB to draw a diagram between the normalized amplitude and frequency ratio for
different damping ratios.
(c) Use MATLAB to draw a diagram between the phase and frequency ratio for different
damping ratios.
(2) Consider a machine base that is supported on some stiffness are excited by a harmonic motion. If
the ratio of the response of the body X to external motion at the base Y can be represented by the
expression:
(a) The response X is ………………….. (transient-steady state) [choose]
(b) Draw the equation at different damping ratios.
(c) Write down the equation that gives the ratio of the forces transmitted due to the base motion.
(3) Consider a forging machine operates at a particular speed, a periodic force is usually generated in
the machine at that frequency. This force gets transmitted in the vertical direction to the base or
foundation of the machine.
(a) Define force transmissibility for this case.
(b) Write down the equation of force transmissibility.
(c) When does the force transmissibility become less than unity?
(4) Give three examples that are used in industry for vibration and force isolation.
(5) For the undamped single degree of freedom mass–spring system shown, let m =
5 kg, k = 2500 N/m, F0 = 20 N, and the force frequency ωf = 18 rad/s. The mass
has the initial conditions x0 = 0.01 m and 𝒙̇ 𝟎 = 1 m/s. Determine the displacement
of the mass at t = 1 s.
Dr Mahmoud Heshmat
(6) The uniform slender bar shown, which has length l and mass m, is pinned at point
O and connected to a linear spring which has a stiffness coefficient k. If the bar is
subjected to the moment M = M0 sin ωft, obtain the steady state response of this
system.
(7) For the single degree of freedom mass–spring system, m =10 kg, k = 4000 N/m, F0 = 40 N, and ω f =
20 rad/s. The initial conditions are x0 = 0.02 m and 𝒙̇ 𝟎 = 0. Determine the displacement of the mass
after t = 0.5 s and t = 1 s.
Dr Mahmoud Heshmat